Problem: $(21+2i)+(13+8i)=$ Express your answer in the form $(a+bi)$.
Solution: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({21}+{2}i)+({13}+{8}i)&={21}+{2}i+{13}+{8}i \\\\ &={21}+{13}+{2}i+{8}i \\\\ &={34}+{10}i \end{aligned}$ Summary $({21}+{2}i)+({13}+{8}i)={34}+{10}i$